The VYGFVRACL (SEQ ID NO:1) peptide is derived from the catalytic sub-unit of the Telomerase protein. (See Meyerson et al., (1997) Cell 90: 785-795 and Nakamura et al., (1997) Science 277: 955-9) These studies describe the near-simultaneous discovery of the DNA and deduced amino acid sequence of the Telomerase catalytic subunit from database sequences. Both studies note that Telomerase catalytic sub-unit activity is associated with human cancer. The Class I HLA molecules of these cancerous cells present peptides from this protein, including VYGFVRACL (SEQ ID NO:1). This peptide is presented in the context of HLA-A24 (Arai et al., (2001) Blood 97 (9): 2903-2907, and Tajima et al., Int. J. Cancer (2004) 110: 403-412). Therefore, the VYGFVRACL (SEQ ID NO:1)-HLA-A24 complex provides a cancer marker that the TCRs of the invention can target, for example for the purpose of delivering cytotoxic agents to the cancer cells.